[amluto]

There’s no free lunch.

The sun radiates heat like a blackbody sphere with the surface area of the sun and a surface temperature of 5600K or so.

If the Earth were to have a fancy heat pump that radiated the same amount of heat into space, it would need the radiating area times the effective temperature to the fourth power equal to that of the sun. The real killer problem is that your heat pump is subject to the Carnot efficiency of pumping heat to that same temperature.

By the most straightforward Second Law calculation, entropy transferred to hot side >= entropy removed from cold side. So Q_hot / T_hot >= Q_cold / T_cold. Q_cold is the heat removed from the pleasant ~300K place where the humans are. At 5600K on the hot side, 18.6 times as much heat needs to be radiated out, so for every bit of useful work done on Earth, at least 17.6 times as much energy is consumed in cooling. If you want the radiator to be only half the surface area of the sun, multiply that by about 16.

What future humans really need is a Dyson sphere with absolutely enormous radiating area. :)

[anon____]

Well then maybe we should do this at night, i.e. always on the dark side of the Earth, not the one that's facing the Sun. Basically passing through the radiation that reaches us.

[pyinstallwoes]

Like space itself